SELF-SIMILARITY IN COMPLEX NETWORKS: FROM THE VIEW OF THE HUB REPULSION

2013 ◽  
Vol 27 (28) ◽  
pp. 1350201 ◽  
Author(s):  
HAIXIN ZHANG ◽  
XIN LAN ◽  
DAIJUN WEI ◽  
SANKARAN MAHADEVAN ◽  
YONG DENG
Keyword(s):  
Fractal Dimension ◽  
Complex Systems ◽  
Complex Networks ◽  
Fractal Structure ◽  
The Self ◽  
New Method ◽  
Self Similarity ◽  
Nature And Society ◽  
Real Complex

Complex networks are widely used to model the structure of many complex systems in nature and society. Recently, fractal and self-similarity of complex networks have attracted much attention. It is observed that hub repulsion is the key principle that leads to the fractal structure of networks. Based on the principle of hub repulsion, the metric in complex networks is redefined and a new method to calculate the fractal dimension of complex networks is proposed in this paper. Some real complex networks are investigated and the results are illustrated to show the self-similarity of complex networks.

scholarly journals After notes on self-similarity exponent for fractal structures

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 440-448 ◽  
Author(s):  
Manuel Fernández-Martínez ◽  
Manuel Caravaca Garratón
Keyword(s):  
Fractal Dimension ◽  
Broad Spectrum ◽  
Fractal Structure ◽  
Similarity Index ◽  
Random Processes ◽  
The Self ◽  
Sample Function ◽  
Fractal Structures ◽  
Self Similarity ◽  
Image Set

AbstractPrevious works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.

Fractal Characteristic of Electrical Trees Grown in Silicone Rubber under Environmental Stress

2017 ◽  
Vol 7 (3) ◽  
pp. 1628
Author(s):  
M. S. Mohd Fua’ad ◽  
M.H. Ahmad ◽  
Y. Z. Arief ◽  
N. A. Ahmad
Keyword(s):  
Fractal Dimension ◽  
Fractal Structure ◽  
The Self ◽  
Fractal Structures ◽  
Self Similarity ◽  
Fractal Characteristic ◽  
Electrical Tree ◽  
Breakdown Phenomenon ◽  
Electrical Trees ◽  
Electrical Treeing

<div class="WordSection1"><p>One of the degradations of insulation is in the form of electrical treeing in which classified as a pre-breakdown phenomenon of electrical insulation. The electrical tree is commonly forming in the shape of tree-like or root-like which may have fractal structures. Due to this fractal structure, electrical treeing formation and patterns are analysed via fractal dimension and lacunarity to study the self-similarity patterns of electrical treeing. Many types of research have been conducted to study the fractal dimension and lacunarity of electrical treeing to fully understand the electrical tree mechanism and characteristics. However, fractal and lacunarity structures of</p></div>

scholarly journals A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters

2021 ◽  
Vol 35 (4) ◽  
pp. 1197-1210
Author(s):  
C. Giudicianni ◽  
A. Di Nardo ◽  
R. Greco ◽  
A. Scala
Keyword(s):  
Fractal Dimension ◽  
Community Structure ◽  
Distribution Systems ◽  
Water Distribution ◽  
Scaling Law ◽  
Vulnerability Index ◽  
The Self ◽  
Node Degree ◽  
Specific Response ◽  
Self Similarity

AbstractMost real-world networks, from the World-Wide-Web to biological systems, are known to have common structural properties. A remarkable point is fractality, which suggests the self-similarity across scales of the network structure of these complex systems. Managing the computational complexity for detecting the self-similarity of big-sized systems represents a crucial problem. In this paper, a novel algorithm for revealing the fractality, that exploits the community structure principle, is proposed and then applied to several water distribution systems (WDSs) of different size, unveiling a self-similar feature of their layouts. A scaling-law relationship, linking the number of clusters necessary for covering the network and their average size is defined, the exponent of which represents the fractal dimension. The self-similarity is then investigated as a proxy of recurrent and specific response to multiple random pipe failures – like during natural disasters – pointing out a specific global vulnerability for each WDS. A novel vulnerability index, called Cut-Vulnerability is introduced as the ratio between the fractal dimension and the average node degree, and its relationships with the number of randomly removed pipes necessary to disconnect the network and with some topological metrics are investigated. The analysis shows the effectiveness of the novel index in describing the global vulnerability of WDSs.

A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions

2018 ◽  
Vol 33 (10) ◽  
pp. 1850057 ◽  
Author(s):  
I. Zborovský
Keyword(s):  
Conservation Law ◽  
Fractal Structure ◽  
Fractal Dimensions ◽  
The Self ◽  
Hadron Structure ◽  
Self Similarity ◽  
Similarity Variable ◽  
Variable Formula ◽  
Entropy Principle ◽  
Fragmentation Processes

Fractal self-similarity of hadron interactions demonstrated by the [Formula: see text]-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable [Formula: see text] is a function of the momentum fractions [Formula: see text] and [Formula: see text] of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions [Formula: see text] and [Formula: see text] of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the [Formula: see text]-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

ECCENTRIC DISTANCE SUM OF SIERPIŃSKI GASKET AND SIERPIŃSKI NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950016 ◽  
Author(s):  
JIN CHEN ◽  
LONG HE ◽  
QIN WANG
Keyword(s):  
Asymptotic Formula ◽  
Complex Networks ◽  
Sierpinski Gasket ◽  
The Self ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Similar Measure ◽  
Self Similar ◽  
Eccentric Distance

The eccentric distance sum is concerned with complex networks. To obtain the asymptotic formula of eccentric distance sum on growing Sierpiński networks, we study some nonlinear integral in terms of self-similar measure on the Sierpiński gasket and use the self-similarity of distance and measure to obtain the exact value of this integral.

scholarly journals Rock Mechanical Property Influenced by Inhomogeneity

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yunliang Tan ◽  
Dongmei Huang ◽  
Ze Zhang
Keyword(s):  
Mechanical Property ◽  
Fractal Dimension ◽  
Rock Type ◽  
Fractal Dimensions ◽  
Rock Material ◽  
The Self ◽  
Self Similarity ◽  
Red Sandstone ◽  
Variation Patterns ◽  
Rock Microstructure

In order to identify the microstructure inhomogeneity influence on rock mechanical property, SEM scanning test and fractal dimension estimation were adopted. The investigations showed that the self-similarity of rock microstructure markedly changes with the scanned microscale. Different rocks behave in different fractal dimension variation patterns with the scanned magnification, so it is conditional to adopt fractal dimension to describe rock material. Grey diabase and black diabase have high suitability; red sandstone has low suitability. The suitability of fractal-dimension-describing method for rocks depends on both investigating scale and rock type. The homogeneities of grey diabase, black diabase, grey sandstone, and red sandstone are 7.8, 5.7, 4.4, and 3.4, separately; their average fractal dimensions of microstructure are 2.06, 2.03, 1.72, and 1.40 correspondingly, so the homogeneity is well consistent with fractal dimension. For rock material, the stronger brittleness is, the less profile fractal dimension is. In a sense, brittleness is an image of rock inhomogeneity in macroscale, while profile fractal dimension is an image of rock inhomogeneity in microscale. To combine the test of brittleness with the estimation of fractal dimension with condition will be an effective approach for understanding rock failure mechanism, patterns, and behaviours.

Modeling the self-similarity in complex networks based on Coulomb’s law

2016 ◽  
Vol 35 ◽  
pp. 97-104 ◽  
Author(s):  
Haixin Zhang ◽  
Daijun Wei ◽  
Yong Hu ◽  
Xin Lan ◽  
Yong Deng
Keyword(s):  
Complex Networks ◽  
The Self ◽  
Self Similarity ◽  
Coulomb’S Law ◽  
Coulomb's Law

A Modified Box-Counting Method to Estimate the Fractal Dimensions

2011 ◽  
Vol 58-60 ◽  
pp. 1756-1761 ◽  
Author(s):  
Jie Xu ◽  
Giusepe Lacidogna
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
The Self ◽  
Whole Body ◽  
Counting Method ◽  
Border Effect ◽  
Self Similarity ◽  
Box Counting ◽  
Self Similar ◽  
Box Counting Method

A fractal is a property of self-similarity, each small part of the fractal object is similar to the whole body. The traditional box-counting method (TBCM) to estimate fractal dimension can not reflect the self-similar property of the fractal and leads to two major problems, the border effect and noninteger values of box size. The modified box-counting method (MBCM), proposed in this study, not only eliminate the shortcomings of the TBCM, but also reflects the physical meaning about the self-similar of the fractal. The applications of MBCM shows a good estimation compared with the theoretical ones, which the biggest difference is smaller than 5%.

A New Method of Characterization on Microstructure of Casting Alloy

2011 ◽  
Vol 211-212 ◽  
pp. 122-126
Author(s):  
Zheng Liu ◽  
Xiao Mei Liu
Keyword(s):  
Fractal Dimension ◽  
Fractal Structure ◽  
A356 Alloy ◽  
Fractal Dimensions ◽  
Primary Phase ◽  
New Method ◽  
Casting Alloy ◽  
Microstructural Characteristics ◽  
Low Superheat

Microstructural characteristics of A356 alloy prepared by low superheat pouring were researched, and the fractal dimensions of morphology of primary phase in the alloy was calculated. The results indicated that morphology of primary phase in A356 alloy belonged to fractal structure, and the microstructural characteristics in the alloy can be characterized by fractal dimension. There were the different fractal dimensions for the morphology of primary phase prepared by the different process.

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